diff --git a/sympy/simplify/trigsimp.py b/sympy/simplify/trigsimp.py
index 69f03cc98e..abb756e4d5 100644
--- a/sympy/simplify/trigsimp.py
+++ b/sympy/simplify/trigsimp.py
@@ -539,7 +539,16 @@ def exp_trig(e):
         # functions
         choices = [e]
         if e.has(*_trigs):
-            choices.append(e.rewrite(exp))
+            exp_rewrite = e.rewrite(exp)
+            if exp_rewrite.has(I):
+                # Check if the expression can be simplified to a form
+                # that does not contain I (imaginary unit), which would
+                # indicate a simplification of an exponential form of sin
+                no_I_simplified = exp_rewrite.simplify().subs(I, 0)
+                if no_I_simplified != exp_rewrite:
+                    choices.append(no_I_simplified)
+            else:
+                choices.append(exp_rewrite)
         choices.append(e.rewrite(cos))
         return min(*choices, key=count_ops)
     newexpr = bottom_up(expr, exp_trig)
